Adiabatic evolution of orbital parameters in Kerr spacetime

Norichika Sago, Takahiro Tanaka, Wataru Hikida, Katsuhiko Ganz, Hiroyuki Nakano

Research output: Contribution to journalArticle

55 Citations (Scopus)

Abstract

We investigate the adiabatic orbital evolution of a point particle in Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is sufficiently smaller than the characteristic timescale of orbits, the evolution of orbits is characterized by the rates of change of three constants of motion, the energy E, the azimuthal angular momentum L, and the Carter constant Q. We can evaluate the rates of change of E and L from the fluxes of the energy and the angular momentum at infinity and on the event horizon, employing the balance argument. However, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. Recently, Mino proposed a new method of evaluating the average rate of change rate of the Carter constant by using the radiative field. In a previous paper, we developed a simplified scheme for determining the evolution of the Carter constant based on Mino's proposal. In this paper we describe our scheme in more detail and derive explicit analytic formulae for the rates of change of the energy, the angular momentum and the Carter constant.

Original languageEnglish
Pages (from-to)873-907
Number of pages35
JournalProgress of Theoretical Physics
Volume115
Issue number5
DOIs
Publication statusPublished - May 1 2006

Fingerprint

orbitals
angular momentum
orbits
event horizon
gravitational waves
infinity
energy
proposals

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

Cite this

Adiabatic evolution of orbital parameters in Kerr spacetime. / Sago, Norichika; Tanaka, Takahiro; Hikida, Wataru; Ganz, Katsuhiko; Nakano, Hiroyuki.

In: Progress of Theoretical Physics, Vol. 115, No. 5, 01.05.2006, p. 873-907.

Research output: Contribution to journalArticle

Sago, Norichika ; Tanaka, Takahiro ; Hikida, Wataru ; Ganz, Katsuhiko ; Nakano, Hiroyuki. / Adiabatic evolution of orbital parameters in Kerr spacetime. In: Progress of Theoretical Physics. 2006 ; Vol. 115, No. 5. pp. 873-907.
@article{a902ccebfcf845edb4d3963a5cc82648,
title = "Adiabatic evolution of orbital parameters in Kerr spacetime",
abstract = "We investigate the adiabatic orbital evolution of a point particle in Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is sufficiently smaller than the characteristic timescale of orbits, the evolution of orbits is characterized by the rates of change of three constants of motion, the energy E, the azimuthal angular momentum L, and the Carter constant Q. We can evaluate the rates of change of E and L from the fluxes of the energy and the angular momentum at infinity and on the event horizon, employing the balance argument. However, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. Recently, Mino proposed a new method of evaluating the average rate of change rate of the Carter constant by using the radiative field. In a previous paper, we developed a simplified scheme for determining the evolution of the Carter constant based on Mino's proposal. In this paper we describe our scheme in more detail and derive explicit analytic formulae for the rates of change of the energy, the angular momentum and the Carter constant.",
author = "Norichika Sago and Takahiro Tanaka and Wataru Hikida and Katsuhiko Ganz and Hiroyuki Nakano",
year = "2006",
month = "5",
day = "1",
doi = "10.1143/PTP.115.873",
language = "English",
volume = "115",
pages = "873--907",
journal = "Progress of Theoretical Physics",
issn = "0033-068X",
publisher = "Published for the Research Institute for Fundamental Physics by Physical Society of Japan",
number = "5",

}

TY - JOUR

T1 - Adiabatic evolution of orbital parameters in Kerr spacetime

AU - Sago, Norichika

AU - Tanaka, Takahiro

AU - Hikida, Wataru

AU - Ganz, Katsuhiko

AU - Nakano, Hiroyuki

PY - 2006/5/1

Y1 - 2006/5/1

N2 - We investigate the adiabatic orbital evolution of a point particle in Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is sufficiently smaller than the characteristic timescale of orbits, the evolution of orbits is characterized by the rates of change of three constants of motion, the energy E, the azimuthal angular momentum L, and the Carter constant Q. We can evaluate the rates of change of E and L from the fluxes of the energy and the angular momentum at infinity and on the event horizon, employing the balance argument. However, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. Recently, Mino proposed a new method of evaluating the average rate of change rate of the Carter constant by using the radiative field. In a previous paper, we developed a simplified scheme for determining the evolution of the Carter constant based on Mino's proposal. In this paper we describe our scheme in more detail and derive explicit analytic formulae for the rates of change of the energy, the angular momentum and the Carter constant.

AB - We investigate the adiabatic orbital evolution of a point particle in Kerr spacetime due to the emission of gravitational waves. In the case that the timescale of the orbital evolution is sufficiently smaller than the characteristic timescale of orbits, the evolution of orbits is characterized by the rates of change of three constants of motion, the energy E, the azimuthal angular momentum L, and the Carter constant Q. We can evaluate the rates of change of E and L from the fluxes of the energy and the angular momentum at infinity and on the event horizon, employing the balance argument. However, for the Carter constant, we cannot use the balance argument because we do not know the conserved current associated with it. Recently, Mino proposed a new method of evaluating the average rate of change rate of the Carter constant by using the radiative field. In a previous paper, we developed a simplified scheme for determining the evolution of the Carter constant based on Mino's proposal. In this paper we describe our scheme in more detail and derive explicit analytic formulae for the rates of change of the energy, the angular momentum and the Carter constant.

UR - http://www.scopus.com/inward/record.url?scp=33747737961&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747737961&partnerID=8YFLogxK

U2 - 10.1143/PTP.115.873

DO - 10.1143/PTP.115.873

M3 - Article

AN - SCOPUS:33747737961

VL - 115

SP - 873

EP - 907

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 5

ER -